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# st: testing fixed effects versus random effects for clustered data using overiden

 From Ridhima Gupta To statalist@hsphsun2.harvard.edu Subject st: testing fixed effects versus random effects for clustered data using overiden Date Mon, 28 Feb 2011 14:46:15 +0000

```Hello,

I don't have a panel data in the strict sense of the term i.e. I have
data on farmers who have several plots/fields. I first perform a
standard hausman test and I do not reject the
null hypothesis of random effects. The result is as follows:

hausman fixed ., sigmamore

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|     fixed          .          Difference          S.E.
-------------+----------------------------------------------------------------
Happy_Seeder |    .1271123     .5428827       -.4157704         .429518
Rotavator |   -.3621306    -.3157851       -.0463455         .840699
Seed_Drill |    -.083707      .860967        -.944674        .5539517
quantity_s~c |    .0056369    -.0031733        .0088101        .0188915
plotsize_hec |    .0252054     .0310519       -.0058465        .0525993
ferti_hec |    .0027516      .003003       -.0002514        .0045816
exp_weedi_~s |    .1077859     .0282141        .0795719        .0585852
soil_type_1 |   -1.034988    -1.900228        .8652395        .6801256
soil_type_2 |   -.4202215    -2.165068        1.744846        .8051986
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test:  Ho:  difference in coefficients not systematic

chi2(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=       12.70
Prob>chi2 =      0.1766

But when I perform the robust version of this test, I reject the null
hypothesis of random effects.

Random-effects GLS regression                   Number of obs      =       227
Group variable: hh_id                           Number of groups   =        86

R-sq:  within  = 0.0106                         Obs per group: min =         1
between = 0.0922                                        avg =       2.6
overall = 0.0674                                        max =         6

Random effects u_i ~ Gaussian                   Wald chi2(9)       =     15.76
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =    0.0720

(Std. Err. adjusted for 86 clusters in hh_id)
------------------------------------------------------------------------------
|               Robust
yield_per_~c |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Happy_Seeder |   .5428827   1.024596     0.53   0.596    -1.465289    2.551054
Rotavator |  -.3157851   1.425605    -0.22   0.825     -3.10992     2.47835
Seed_Drill |    .860967   1.036252     0.83   0.406    -1.170049    2.891983
quantity_s~c |  -.0031733    .041733    -0.08   0.939    -.0849685     .078622
plotsize_hec |   .0310519   .0467653     0.66   0.507    -.0606065    .1227103
ferti_hec |    .003003   .0053299     0.56   0.573    -.0074435    .0134495
exp_weedi_~s |   .0282141   .0792311     0.36   0.722    -.1270759    .1835041
soil_type_1 |  -1.900228   .7639786    -2.49   0.013    -3.397599   -.4028574
soil_type_2 |  -2.165068   .8668351    -2.50   0.013    -3.864033   -.4661022
_cons |   41.85728   4.370738     9.58   0.000     33.29079    50.42376
-------------+----------------------------------------------------------------
sigma_u |  4.4041886
sigma_e |  4.0351113
rho |  .54364968   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtoverid

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re  robust cluster(hh_id)
Sargan-Hansen statistic  26.327  Chi-sq(9)    P-value = 0.0018

Is there any inconsistency here? Are there any tests in the literature
that allow me to test the assumption of homoskedasticity and no
auto-correlation in the random effects model?

Thanks a lot,
Ridhima
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```